Question

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 100 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 10 to year 20.

The crop yield increased by 200 pounds per acre from year 10 to year 20.
The crop yield increased by 100 pounds per acre from year 10 to year 20.
The crop yield decreased by 10 pounds per acre from year 10 to year 20.
The crop yield decreased by 0.1 pounds per acre from year 10 to year 20.

Answer 1

'The crop yield decreased by 10 pounds per acre from year 10 to year 20.'

Explanation:

i got it right on the test =)

Answer 2

The average rate of change = -10

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Explanation:

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function
`f(x) =-x^2 + 20x + 100` models the crops in pounds per acre over x years.

The average rate of change can be calculated using formula

`(f(b)-f(a))/(b-a)`

In your case,

`a=10\\ \\b=20,`

then

`f(a)=-10^2+20\cdot 10+100=-100+200+100=200\\ \\f(b)=-20^2+20\cdot 20+100=-400+400+100=100`

and the average rate of change is

`(100-200)/(20-10)=(-100)/(10)=-10`

This means the crop yield decreased by 10 pounds per acre (negative rate of change) from year 10 to year 20.